1. The problem is to find the range of the function $y = x^2$. 2. The function $y = x^2$ is a quadratic function where $x$ can be any real number. 3. The formula for the function is $y = x^2$. 4. Since squaring any real number $x$ results in a non-negative value, $y$ is always greater than or equal to 0. 5. The smallest value of $y$ is 0, which occurs when $x = 0$. 6. As $x$ moves away from 0 in either positive or negative direction, $y$ increases without bound. 7. Therefore, the range of $y = x^2$ is all real numbers $y$ such that $y \geq 0$. Final answer: The range of $y = x^2$ is $[0, \infty)$.